In this section, we formulate the passive quantum detector given multiple copies from the same unknown target system. Let \(\rho \in \mathcal {S}\)  be the density operator of the unknown target system. We assume the scenario of binary hypothesis testing [1]}, that is, only one density matrix is included under \(H_0,H_1\)  respectively:
\(H_0:\rho = \rho _0,\; H_1:\rho = \rho _1,\) 
